Realizing the relaxion from multiple axions and its UV completion with high scale supersymmetry

Abstract

Abstract: We discuss a scheme to implement the relaxion solution to the hierarchy problem with multiple axions, and present a UV-completed model realizing the scheme. All of the N axions in our model are periodic with a similar decay constant f well below the Planck scale. In the limit N ≫ 1, the relaxion ϕ corresponds to an exponentially long multi-helical flat direction which is shaped by a series of mass mixing between nearby axions in the compact field space of N axions. With the length of flat direction given by Δϕ = 2πfeff ∼ eξNf for ξ=O(1), both the scalar potential driving the evolution of φ during the inflationary epoch and the ϕ-dependent Higgs boson mass vary with an exponentially large periodicity of O(f)eff, while the back reaction potential stabilizing the relaxion has a periodicity of Of O(f). A natural UV completion of our scheme can be found in high scale or (mini) split supersymmetry (SUSY) scenario with the axion scales generated by SUSY breaking as f∼mSUSYM∗, where the soft SUSY breaking scalar mass mSUSY can be well above the weak scale, and the fundamental scale M* can be identified as the Planck scale or the GUT scale. © 2016, The Author(s)